Dog pee on hardwood floor is a nasty situation and can possibly mess up the wood. I have researched your question and I came across a great link that can help you remove the stain. I have attached the link below for you to view. I hope the link that I have provided you is helpful.

Depending on how severe the urine stains are on your hardwood floor, the attached link gives you a step by step process to try. See if this process works, taking it slow and working with the process over the course of several days to weeks. The recommeded process does not remove the stain, it lightens it over time so the stained area blends better with the rest of the floor. If this doesn't work, then the stains have penetrated much deeper. Sanding the floor, refinishing and sealing might be in order. Worse case if sanding doesn't work, a professional can cut the piece of stained flooring out and replace it with new flooring.